Supplementary Material T1

In this supplementary material section we provide the computational details and references for the different methods and programs used in each submission.

Entry A

All results were computed on the basis of the CBS-QB3 composite method,[1, 2] without geometry constraints and with a frequency analysis to conﬁrm the nature of the stationary points. The ZPVE was computed from the harmonic frequencies, as deﬁned by the composite method. All calculations were performed with the Gaussian 09 program package[3].

Entry B

All dimers were optimized without any geometry constraint at the ωB97xD/6-311G(df,pd) level of theory[4], which includes dispersion corrections according to the original formulation of Grimme[5]. The nature of all stationary points was conﬁrmed by a frequency analysis. The ZPVE correction was provided at the same level of theory. The ﬁnal electronic energies include a counterpoise correction according to the scheme proposed by Boys and Bernardi[6].

Entry C

The geometries of the different compounds were optimised using the B3LYP-D3(BJ)/aug-cc-pVTZ level of theory[7, 8, 9, 10, 11] as implemented in ORCA[12]. The RIJCOSX approximation[13] was used along with a cc-pVTZ/JK auxiliary basis set to speed up calculations. The nature of each minima was double checked using a harmonic vibrational analysis at the same level of theory. The anharmonic calculations were done using the Pvscf program[14, 15] and are based on the vibrational self-consistent field method (VSCF). The calculation used the computed B3LYP-D3(BJ)/aug-cc-pVTZ Hessian matrices to determine normal modes, which were represented in curvilinear coordinates. A multilayer approach was used to generate an accurate potential energy surface where both 1-mode and 2-modes couplings were computed at the HF-3c level of theory,[16] as this approach has been shown to be both fast and accurate. However, to ensure accuracy, the 1-mode couplings were recomputed using a DLPNO-CCSD(T) approach[17, 18, 19, 20] with extrapolation to the basis set limit based on RI-MP2 data obtained for the aug-ano-pVTZ and aug-ano- PVQZ basis sets. The anharmonic mode-mode coupling is represented through a reduced coupling scheme (STA)[21, 22]. Vibrational correlation effects are included using state-specific vibrational configuration interaction (VCI) coupled with a perturbative screening of the VCI space. As a test of the method, the anharmonic OH stretch of a free methanol molecule obtained using this approach is 3688 cm−1, which is within 4 cm−1 of the measured experimental value (3684 cm−1)[23]. Due to time limitations, the anharmonic transition dipole intensities were computed using a 1D dipole surface calculated at the HF/aug-ano-pVQZ level of theory along with a diagonal approximation (1D, no couplings) for the vibrational wave function. All dimer energies were computed at the DLPNO- CCSD(T)/aug-ano-pV5Z level of theory using full counterpoise basis-set superposition error correction.

1 Entry D

Use was made of a composite scheme developed over the last decade to investigate the spectroscopy and the dynamics of weakly bound molecular systems. This scheme combines the use of the PBE0 functional[24], Grimme’s D3 dispersion correction[11] and the recently launched explicitly correlated coupled cluster method (CCSD(T)-F12)) technique[25]. First, full geometry optimizations were performed for all complexes as provided by Poblotzki et al[26]. These computations were carried out in the C1 point group at the PBE0-D3/aug-cc-pVTZ level[7, 8, 9] as implemented in the Gaussian09 program package[3]. Harmonic frequency calculations were carried out to check the nature of the stationary points (minimum or transition state) and to evaluate the zero-point vibrational energy (ZPE) corrections of the considered molecular clusters. Single point computations using the CCSD(T)-F12 method were then performed whereby the aug-cc-pVTZ basis set was used in conjunction with the corresponding resolutions of the identity and density ﬁtting functions as generated by MOLPRO (Version 2015.1)[27]. These computations were done with the PBE0/aug-cc-pVTZ optimized geometries.

Entry E

Geometries and harmonic frequencies were calculated at the DFT level, using the B3LYP exchange correlation functional.[10] The D3-dispersion correction with Becke-Johnson damping was included in all cases[11]. The def2-QZVPPD basis set was used for all atoms. In all cases, a very ﬁne integration grid (grid6) was used. A tight optimization criterion was used for geometry optimizations. ZPE corrections were calculated using the harmonic approximation. Single-point DLPNO-CCSD(T) calculations were carried out with TightPNO settings, using the fully linear scaling implementation[20]. Unless otherwise speciﬁed, Dunning’s correlation-consistent cc-pV5Z basis sets and matching correlation auxiliary basis were used[7, 8]. All calculations were carried out with the Orca program package[12].

Entry F

The protocol used for calculating zero-point corrected energies is subdivided into four steps. In step one geometry optimizations were performed with SCS(cos=1.1, css=0.6)-MP2/aug-cc-pVQZ[28, 8, 29] employing the modiﬁed spin scaling parameters of cOS=1.1 and cSS=0.6 as suggested by Risthaus et al[30]. Using the optimized geometries in the next step, harmonic frequency calculations were performed at the same level of theory to evaluate the ZPE contribution. Both geometry optimizations and frequency calculations, were executed using the Turbomole 7.0.2 program package[31, 32]. The resolution-of-identity (RI) approximation for the Coulomb integrals was applied (at least for geometry optimization and frequency calculation) using matching default auxiliary basis sets[33]. Step three accounts for highly accurate electronic energies using the nonrelativistic W2-F12 protocol[34], excluding ZPE, on the SCS-MP2 geometries employing the MOLPRO 2012.1.0 program[35]. Step four (anharmonic corrections): to obtain the anharmonic zero-point vibrational energy correction, the standard perturbation based approach to anharmonic vibrations[36, 37] in full dimensionality

2 as implemented in the Gaussian 09 software[3] is applied. In order to make these calculations practi- cable, the SVWN[38, 39] local density functional is used together with Dunnings DZ basis set[40] as obtained from the EMSL basis set exchange database[29]. The SVWN/DZ optimizations were started from the SCS(1.1;0.6)-MP2/aug-cc-pVQZ geometries. The anharmonic ZPVE correction was obtained by scaling the harmonic ZPVE correction at the SCS(1.1;2/3)-MP2/aug-cc-pVQZ level of theory by the ratio of the anharmonic to the harmonic ZPVE correction at the SVWN/DZ level of theory. In the end, the zero point corrected single point energies were comprised of the W2-F12 electronic energies, the SCS(cos=1.1,css=0.6)-MP2 zero point corrections and respective anharmonic corrections. The frequencies of the methanol OH stretching vibration (shown in Table IV in the manuscript) were calculated by distorting the molecules along this normal mode with the interactive module vibration of Turbomole[32]. Single point energy calculations are performed at the same level as used for geometry optimization (but without the RI approximation for the Coulomb integrals). The time-independent Schrödinger equation in the one dimensional potential is solved with the WavePacket program[41] using the deviation of the methanol OH bond distance from its equilibrium value as independent variable. The size of the grid was ±1.5 a.u., ensuring that the resulting wave functions ïňĄt into the grid in real and momentum space. The mass used was the reduced mass of oxygen and hydrogen. The frequency of the methanol OH stretching fundamental is the diﬀerence between the energies of the ﬁrst excited state and the ground state (details to the employed method can be found here[42]).

Entry G

All structures were optimized with the PBE0-D3 method,[24, 11] using a custom basis set which will be denoted as ‘QZVG’. It consists of the standard QZVP basis[43] substituting the (3d2f1g) polarization functions set with the (2d1f) set of def2-TZVP for the C and O atoms. In the case of hydrogen, the (3p2d1f) set was replaced by the (2p1d) set from the def2-TZVP basis. The optimizations were carried out with the Turbomole program, using a ‘m5’ quality integration grid. Self-consistent field convergence −9 thresholds ‘scfconv’ and ‘deconv’ were reduced to 10 Eh. Geometry optimization thresholds ‘energy’ and ‘gcart’ were reduced to 10−8 and 10−4 respectively. No resolution-of-the-identity approximations were used, nor counterpoise corrections were applied. The interaction energies of the dimers were computed by the use of DFT-SAPT,[44] with the PBE0 exchange-correlation functional and the standard Leeuwen-Baerends (LB94) asymptotic correction[45]. The shift parameter in the asymptotic correction was determined from the energy of the HOMO of the geometry-optimized free monomers (using the same PBE0-D3/QZVG level as described above) and the ionization potential calculated as energy difference between the neutral monomers and their respective cations (the latter described with unrestricted Kohn- Sham DFT using the geometry of the neutral parent system). Complete basis set (CBS) extrapolations were carried out for the dispersion and exchange-dispersion contributions using the standard Halkier et al.[46] X−3 expression for electron correlation contributions for X = (T,Q) and assuming that all other contributions are already converged for X = Q. ∆HF estimates of the higher-order induction and exchange-induction contributions were determined from counterpoise-corrected supermolecular Hartree- Fock interaction energies and Hartree-Fock-level SAPT calculations of the first-order and second-order

3 induction and exchange-induction contributions.

Entry H

The same procedures as in Entry G were used, except PBE0 was systematically replaced with B3LYP[10] in all DFT+D geometry optimizations and all DFT-SAPT computations (including determination of the asymptotic correction parameters of the exchange-correlation potential).

Entry I

The geometries of all isomers were optimized using SCS-CC2/def2-TZVP and thresholds of 10−6 Eh for −4 changes in total energy and 10 Eh/a0 for changes in gradient. All minima were confirmed by vibrational frequency analysis. The ZPVE for all geometries was also obtained at the SCS-CC2/def2-TZVP level of theory. For evaluating the relative energies at each obtained geometry the following calculations were performed: CCSD(F12)(2*B)/cc-pVQZ-F12 and CCSD(T)/cc-pVQZ-F12. The final energies were obtained by summing up the HF + CABS + CCSD(F12) + (T) contributions at each geometry point and basis set level. From these the difference in electronic energy ∆E was calculated. In the case of Fu and MFu the same calculations were also carried out with the larger cc-pVQZ-F12 basis set. The differences between the two basis sets were found to be below 0.15 kJ/mol. All values presented in the main manuscript refer to the calculations using the largest basis set, cc-pVQZ-F12 for Fu and MFu, cc-pVTZ-F12 for DMFu. The ZPVE was calculated under the harmonic oscillator approximation. All correlation calculations made use of the frozen-core approximation with a freezing point of −3.0 Eh. The standard ‘cbas’ fitting basis sets cc-pVXZ-F12 (X=T or Q) were used for Coulomb fitting. For explicitly correlated F12 calculations the matching cc-pVXZ-F12i ‘cabs’ basis sets were used. For F12 calculations a γ of 1.0 and 1.1 was chosen for VTZ and VQZ respectively. All calculations were carried out with the TURBOMOLE V7.1 program package[31, 32].

Entry J

The optimizations were carried out at the CCSD(T) level of theory, using the aug-cc-pVTZ basis set for −7 the Fu system, and the aug-cc-pVDZ basis for MFu and DMFu. The thresholds used were 10 Eh and −5 10 Eh/a0 for changes in energies and gradient, respectively. All other steps in the calculations were the same as in entry I, including the ZPVE correction which was obtained with the SCS-CC2/def2-TZVP method (value taken from the latter calculations). The CCSD(T) optimizations were carried out with the CFOUR program package. All other calculations were performed with the TURBOMOLE V7.1 program package.

Entry K

Geometries and harmonic vibrational frequencies were determined at the B2PLYP-D3/6-311++g(d,p) level[47] using the Gaussian09.d01 software[3]. All DFT calculations used a very ﬁne grid (199 radial −11 shells and 974 angular points per atom). SCF convergence criteria were set to 10 Eh except for

4 methanol binding to 2,5-MeFu at the oxygen where convergence couldn’t be achieved. In the latter case, −9 convergence was set to 10 Eh at least. An approximated CCSD(T) scheme was employed to calculate single-point energies for the geometries obtained as described above - the domain-based local pair of natural orbital (DLPNO) scheme[20]. The calculations were conducted with the ORCA software[12]. The DLPNO-CCSD(T) level of theory with def2-TZVPP and def2-QZVPP basis sets was employed. ‘Tight’ settings for the DLPNO calculations were used corresponding to ‘TCutPairs’ 10−5, ‘TCutPNO’ 10−7 and ‘TCutMKN’ 10−4 in the ‘mdci’ section. The Hartree-Fock and the correlation energies were extrapolated separately according to EQZ,HF ECBS,HF = ETZ,HF + √ √ e[7.88( 4− 3)−1] EQZ,corr E = 32.97 · E − 42.97 · CBS,corr TZ,corr 32.97 − 42.97

Entry L

The same procedure as in K was followed, with the exception that the ZPVE was computed with an hindered rotor model. In order to account for hindered rotation of the methanol with respect to the ring, a scan was performed on the dihedral angle formed by the methanol oxygen and carbon, the atom of the ring to which the bonding takes place (that has the shortest distance to the methanol oxygen) and the carbon neighbored to it. Scans were performed with a maximum stepsize of 15 degrees. ZPVEs were obtained from the python package TAMkin[48]. On the one hand, RRHO ZPVEs were obtained from the vibrational calculations as described above for the energetic minimum structure and higher- energy conformations. On the other hand, hindered rotor (HR) ZPVEs were obtained for the rotation of the methanol with respect to the furan ring. This hindered rotation links the conformations that were treated separately in the RRHO approach. A fourier series was fitted to represent the potential energy as a function of the scanned dihedral angle. The number of fourier functions was varied to obtain a good compromise between avoidance of oscillations and deviation from the calculated energies. Then, torsional eigenenergies were obtained from solving the torsional Schroedinger equation in terms of fourier- type basis functions. 200 basis functions were sufficient since the focus was not on the free rotor regime at high temperatures but rather on the ZPE at 0K. The ZPE that would correspond to a harmonic oscillator that fits the curvature at the minimum of the potential energy curve was substracted and then the corresponding hindered-rotor ZPE was added.

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